HENRI POINCARE AS AN INVESTIGATOR 221 



He seems from his memoirs and papers, however, also to be equally of 

 the visual and the symbolic types. He valued words highly, and his 

 style is a mountain brook descending from rarefied heights, its clear 

 current here falling over rocks, there gliding smoothly down. His 

 thought is a penetrating ray that illuminates the deepest recesses of the 

 wilderness of phenomena. 



But in any case, whether one be analyst, physicist, biologist or 

 psychologist, the characteristic trait of the intuition is the direct appre- 

 ciation of relationships between the objects of thought, which unite 

 them into a complete structure, unitary in character and harmonious 

 in form. We might define intuition as that power of the mind by 

 which we build the great theories and fit phenomena into a plan 

 designed along the lines of unifying principles. To be more exact, 

 the mind creates a world of its own. This world is conditioned by 

 what we call the outside world, but in many respects we are free to 

 make it what we please, just as the architect is free to create his build- 

 ing although his material limits him. However, we endeavor to create 

 this world with the maximum simplicity, mainly because simplicity 

 implies harmony, that is, beauty. We are not satisfied with what 

 William James called the " blooming confusion of consciousness " but 

 we construct a replica of this consciousness which is simpler. Of two 

 ways we can construct the replica, we choose the simpler. Thus we 

 choose Euclidean geometry instead of Lobatchevskian, on account of its 

 simplicity, although either might be applied to the world of phenomena. 

 We choose to say the earth rotates on its axis, for that makes astronomy 

 possible. This replica must have a plan, a design, a symmetry, a 

 coherence. Intuition is the perception of this idealized structure. It 

 is akin to the dream of the artist, or the vision of the prophet. Indeed 

 the eminent literary critic, Emile Faguet, calls Poincare a poet. Was 

 it not Sylvester and Kronecker who said that mathematics was essen- 

 tially poetry ! That was as far as they ever got in defining it. In his 

 address on " Analysis and Physics," Poincare says : 



Mathematics has a triple end. It must furnish an instrument for the study 

 of nature. But that is not all, it has a philosophic end; and, I dare to say it, 

 an esthetic end; . . . these two ends [physical and esthetic] are inseparable, and 

 the best way to attain the one is to keep the other in view. 



The mathematician does not build in stone, nor paint on canvas, 

 nor construct a symphony, though his harmonies are in and through 

 all these; his medium is more ethereal; but is his creation therefore 

 the less beautiful? 



Since the intuition is necessary, the first problem of education 

 becomes the conservation and development of this power. Poincare 

 points out that in mathematics, for example, we should not begin with 

 general definitions and laws, nor with rigorous logic in the proofs of 



